I need to prove or disprove that R languages are closed under divison.
I have managed to prove thet CFL are't closed under division. I read in wikipedia that RE languages are closed, but I didn't find ...

Let $\Lambda$ be a lattice with basis, $B$ consisting of vectors $b_i$, so that the elements of $\Lambda$ are of form, $y\in \Lambda \iff y=Bx=\sum_i b_ix_i$ for some $x_i\in\mathbb{Z}$.
My questions ...

A game is played as follows. There is a set $X = \{1, \ldots, n\}$. Player 1 is trying to find a "locally minimal subset" $M \subseteq X$ - that is, player 2 has said that $M$ is good, and also that ...

A 2DORG is the intersection graph of a finite family of rays directed $\to$ or $\uparrow$ in the plane. Such graphs can be recognized effectively (Felsner et al.). A 3DORG is the intersection graph of ...

I'm researching method of biprime number factoring. I have a biprime number 1012322327 * 1115382761 (19 decimal digits= 1129126872111204847). I'd like to know how many iterations (or trials) the best ...

Given the sequence of symbols $A$ (contains ~10,000 symbols) and sequence of blocks $B$ (contains ~3,000 blocks, ~30 symbols inside each block) I need to exclude some blocks from sequence $B$ so that ...

What is the best known algorithmic complexity for computing the spectral radius (largest eigenvalue in magnitude, possibly with respect to some precision and confidence) of a symmetric matrix of size $...

In $\mathbb K[x]$ or $\mathbb K$ where $\mathbb K$ is a ring we can think of multiplication of polynomials as convolution. Over $\mathbb Z$ this line of thought has led to fast integer multiplication ...

Given integers $a,\ell$ and prime $p$ we need to find the roots of the algebraic equation $x^\ell\equiv a\bmod p$. We know there are at most $\ell$ such $x$.
What is the best method to find all such ...

Let $M$ be a non-deterministic Turing machine which recognizes a language $L$, that is, for every input word $u$ there is an accepting computation with input $u$ if and only if $u\in L$. The smallest ...

I have read that the complexity of computing the Minkowski-Sum of $2$ non-convex polygons (through convex decomposition) is $O(m^2 n^2)$, where $m$ and $n$ is the number of vertices of each polygon. ...

Manders and Adleman mention that the computational complexity for binary quadratic Diophantine equations is NP-complete. Has a more specific complexity been claimed for polynomials of the form $Axy + ...

Some computational problems have variants that appear to be harder. For instance, Graph Automorphism (GA) problem has quasi-polynomial time algorithm ( by Babai's Graph Isomorphism result) while the ...

Quantum computing is a very active and rapidly expanding field of research. Many companies and research institutes are spending a lot on this futuristic and potentially game-changing technology. Some ...

Standard factoring problem $\Pi_1$ is 'Given integers $N$ and $M$ is there a factor $d\in[1,M]$ of $N$?'. This is in $NP$ since such a factor is the witness and in $coNP$ since one can check all the ...

The Rabin Cryptosystem derives its basic security assumption on the observation, that computing roots in integer modulo $n$ rings, is as hard as finding the prime decomposition of $n$.
Mathematically ...

This question was first asked by Mehtaab Sawhney in Alex Postnikov's combinatorics class.
Given a rational function $F=P(x_1,...,x_n)/Q(x_1,...,x_n)$ with (say) integer coefficients, it is often of ...

Assume that there exists at least one NP-intermediate decision problem (which, by Ladner's theorem, is equivalent to P being distinct from NP).
Do there exist two NP-intermediate decision problems, $...

In quadratic sieve and number field sieve $x,y\in\mathbb Z$ is solved in congruence $x^2\equiv y^2\bmod N$. Is there an estimate on typical sizes (number of bits in integers) of $x,y$ in these methods ...

Given literals $x_1,\dots,x_n$ how many clauses $C_1,\dots,C_m$ does one need of the type $C_i=y_j\vee y_k\vee y_l$ where $y_l\in\{x_l,\overline x_l\}$ such that the CNF form $C_1\wedge\dots\wedge C_m$...